This invention relates to a process for generating fuzzy cognitive maps from a Monte Carlo simulation-generated Meta Model. Using this invention, one can identify variables that have a positive or negative correlation with a phenomenon. This invention also aids in improving phenomena by moving correlating variables towards targets.
It is difficult to identify those factors that have a significant contribution to the outcome of a phenomenon, a phenomenon such as Apartheid South African politics (see FIG. 7), the behavior of an axle on a car, or the failure of a containment vessel in a nuclear reactor. In the present invention, Applicant uses a process to identify those factors that have a significant contribution to the behavior of a phenomenon by using a computer to create a fuzzy cognitive map (FCM).
A fuzzy cognitive map (FCM), is a graph of an event, function, or process that shows the factors or concepts involved in the event, function, or process, and how those factors/concepts influence each other to create a phenomenon. The FCM includes all the factors or concepts that cause or influence the event, function, or process, and the relationships between the factors/concepts. FCMs have historically been drawn by hand by individual experts based on their knowledge of and experience with the event, function, or process. Using this invention, one can use a computer to generate a FCM.
An example of these factors/concepts can be seen in FIG. 7, which is a fuzzy cognitive map of Apartheid South African politics. In FIG. 7 a short description of each factor is enclosed in an ellipse. The relationships of these factors are shown as arrows connecting the factors. The arrows have a direction and a value between +1 and −1. The value of the number indicates the influence (or causality) of one factor/concept on another factor/concept:                A value >0 means that there is a positive influence or causality (when a factor/concept increases then another factor/concept will increase).        A value <0 means that there is a negative influence or causality (when a factor/concept increases then another factor/concept decreases).        
A computer generated FCM is created from a Meta Model generated from Monte Carlo simulations. A Monte Carlo simulation randomly selects the values for the input variables. Monte Carlo is a random number generation process similar to rolling dice or flipping a coin. These Meta Models create a finite, non-redundant set of rules that state “if A then B, with probability P.” A and B are factors or concepts in the model with P being the direction and magnitude of the arrow showing the influence or causality of A on B.
A meta-model, described in Marczik, J. Principals of Simulation-Based Computer-Aided Engineering, FIM Publications, Barcelona, September 1999 (herein incorporated by reference), page 47, is a stacked matrix consisting of all the inputs and all the outputs from a Monte Carlo simulation. The matrix has a row for each Monte Carlo sample and columns for each input and output that goes into the simulation. Using a Monte Carlo simulation, one can take variability and uncertainty into account for every input variable in a problem. Each Monte Carlo run will have different values for the input variables in an analysis. The value of each input variable is randomly selected from all the values within a range of potential values for that variable. A simulation can have any number of variables. Generally, the more variables that one includes, the more realistic the simulation will be.
The outputs of the Monte Carlo runs are different values as each Monte Carlo run has different inputs. Fifty to one hundred Monte Carlo samples are sufficient to obtain useful statistical information on the outputs.
The Monte Carlo method is independent of the problem being simulated. Each run using Monte Carlo is one analysis of that particular problem, event, function, or process. Each particular type of problem, event, function, or process is analyzed using an equation known as a solver. The process being described is independent of the field of application, however for the process to work the field of application has to have solvers that are known to be accurate in modeling reality. While FCMs have been applied in fields as diverse as politics, economics, medicine, and history; the automatic generation of FCMs using this process is limited to those fields that have accurate solvers (formulas that accurately show interactions). The science and engineering fields are the most likely initial applications for this process. In the present invention, when the terms equation or equations are used, we are referring to solvers.